
The magnetic field and its derivatives at the trapping center are represented by matrices \({B}\) , \({B}_{,i}\) , and \({B}_{,ij}\)  as

B̭ B ,
B̭i B,i ,
2 2 B̭j i B,ij , 

respectively, where \(i\)  and \(j\)  represent spatial variables \(x,y,z\)  and comma in the lower index stands for derivatives with respect to variables following it. Spatial derivatives of magnetic field are normalized by the shortest distance \(\rho \)  between the trapping center and the current carrying region. Such normalization enforces equal units to all matrices \({B}\) , \({B}_{,i}\) , and \({B}_{,ij}\)  which is advantageous for mathematical operations in Appendix .

Lost power as
\(P_L̰ \approx \frac{1}{2} ^_\rho ,\) 
where \(_\rho \)  is the lost power matrix [1]}, [2]}.

